Problem: Solve for $x$ : $ 5|x - 10| - 10 = 6|x - 10| + 5 $
Explanation: Subtract $ {5|x - 10|} $ from both sides: $ \begin{eqnarray} 5|x - 10| - 10 &=& 6|x - 10| + 5 \\ \\ {- 5|x - 10|} && {- 5|x - 10|} \\ \\ -10 &=& 1|x - 10| + 5 \end{eqnarray} $ Subtract $5$ from both sides: $ \begin{eqnarray} -10 &=& 1|x - 10| + 5 \\ \\ {- 5} && {- 5} \\ \\ -15 &=& 1|x - 10| \end{eqnarray} $ Simplify: $ -15 = |x - 10| $ The absolute value cannot be negative. Therefore, there is no solution.